The three-dimensional fundamental equations of elasticity of quasicrystals with extension to quasi-static electric effect are expresses in both differential and variational invariant forms for a ...regular region of quasicrystal material. The principle of conservation of energy is stated for the regular region and the constitutive relations are obtained for the piezoelasticity of material. A theorem is proved for the uniqueness in solutions of the fundamental equations by means of the energy argument. The sufficient boundary and initial conditions are enumerated for the uniqueness. Hamilton’s principle is stated for the regular region and a three-field variational principle is obtained under some constraint conditions. The constraint conditions, which are generally undesirable in computation, are removed by applying an involutory transformation. Then, a unified variational principle is obtained for the regular region, with one or more fixed internal surface of discontinuity. The variational principle operating on all the field variables generates all the fundamental equations of piezoelasticity of quasicrystals under the symmetry conditions of the phonon stress tensor and the initial conditions. The resulting equations, which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions, pave the way to the study of important dislocation, fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials.
The interlayer coupling can be used to engineer the electronic structure of van der Waals heterostructures (superlattices) to obtain properties that are not possible in a single material. So far ...research in heterostructures has been focused on commensurate superlattices with a long-ranged Moiré period. Incommensurate heterostructures with rotational symmetry but not translational symmetry (in analogy to quasicrystals) are not only rare in nature, but also the interlayer interaction has often been assumed to be negligible due to the lack of phase coherence. Here we report the successful growth of quasicrystalline 30° twisted bilayer graphene (30°-tBLG), which is stabilized by the Pt(111) substrate, and reveal its electronic structure. The 30°-tBLG is confirmed by low energy electron diffraction and the intervalley double-resonance Raman mode at 1383 cm−1. Moreover, the emergence of mirrored Dirac cones inside the Brillouin zone of each graphene layer and a gap opening at the zone boundary suggest that these two graphene layers are coupled via a generalized Umklapp scattering mechanism—that is, scattering of a Dirac cone in one graphene layer by the reciprocal lattice vector of the other graphene layer. Our work highlights the important role of interlayer coupling in incommensurate quasicrystalline superlattices, thereby extending band structure engineering to incommensurate superstructures.
In the present investigation, attempts were made to study the effect of Al–Cu–Fe (40 vol%) quasicrystalline (QC) reinforcement on the structure, morphology and phase composition of 6082 Al matrix ...nanocomposites (AMCs) processed through mechanical milling (MM) and spark plasma sintering (SPS). The characterization of these MM and SPSed AMCs was done through X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM). The MM induces microstructural refinement of matrix and partial structural transformation of QC phase to Al13Fe4 approximant phase (a = 1.549 nm, b = 0.808 nm, c = 1.248 nm, α = β = 90°, γ = 107.72°; mC102; C2/m). The presence of (311111) diffraction peak of the QC phase in AMCs confirms the existence of face-centred QC phase even after 50 h of MM. The consolidation of Al-QC at 450 °C (723 K) and 550 °C (823 K) results in the fabrication of AMCs having a density of 2.921 and 3.319 g cm−3 respectively. The compressive yield strength and ultimate strength of these AMCs is ∼519 MPa and 639 MPa respectively. The enhancement in the mechanical properties may be attributed to strong interfacial bonding of the Al matrix and QC reinforcement due to interfacial reactions.
•Face-centred ordered IQC in Al-40IQC NC MM upto 50 h.•Homogenous distribution of IQC in Al-40IQC.•Partial structural transformation of IQC to Al13Fe4 phase in Al-40IQC NC during MM.•Evolution of approximant phases due to interfacial reaction in Al-40IQC NC during SPS.•Enhanced compressive strength due to both direct and indirect strengthening.
Based on the conceptual Al–Cu–(Fe + Co) phase diagram we found an optimal initial composition and developed a method to grow Al–Cu–Fe–Co single-grain quasicrystals. Our original two-stage cooling ...process includes (i) fast cooling of the melt down to the quasicrystalline single phase region with rate of ∼165 K/h to prevent growing of nonquasicrystalline phases in the melt, and (ii) slow cooling down with rate of ∼2–3 K/h to grow large (mm-size) single-grain quasicrystals. As a result a new stable quaternary Al-based icosahedral quasicrystal has been obtained. The chemical composition of the grown quasicrystal determined by both the energy dispersive X-ray analysis and inductively coupled plasma mass spectrometry was Al64.36Cu22.20Co3.05Fe10.39. Powder XRD and selected area electron diffraction were carried out for the phase identification and confirmed the icosahedral structure. The temperature dependencies of the electrical resistance measured on the oriented samples in the temperature range of 1.4 K–300 K is typical for icosahedral quasicrystals.
•We constructed conceptual Al–Cu–(Fe + Co) phase diagram.•We used two-stage cooling process to grow quaternary Al–Cu–Fe–Co quasicrystals.•We grew single-grain icosahedral Al64.36Cu22.20Co3.05Fe10.39 stable quasicrystal.
This paper studied the sliding frictional contact of a one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) coating, where the PEQCs coating is imperfectly bonded to a transversely ...isotropic piezoelectric (PE) substrate. The frequency response functions (FRFs) of displacements and stresses of phonon (phason), electric potentials and electric displacements, are analytically derived by applying double Fourier integral transforms to the general solutions and boundary conditions of the 1D hexagonal PEQCs coating-PE substrate systems. The conjugate gradient method (CGM) is used to obtain the unknown pressure distribution and the discrete convolution-fast Fourier transform technique (DC-FFT) is involved to calculate the contact responses such as displacements and stresses. Numerical results are given to reveal the influences of coating thickness, loading conditions and imperfection indices on the contact behavior, which provide a reference basis for PEQCs coating experimental analysis and intelligent structures (systems) design.
Based on the nonlocal elasticity theory, the static bending deformation of one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) nanoplates is investigated under surface electroelastic ...loadings. The general solutions for the extended displacement and traction vectors of a simply supported and homogeneous PQC nanoplate are derived by solving an eigenvalue problem reduced from the pseudo-Stroh formalism. By utilizing the propagator matrix method, exact closed-form solutions of multilayered 1D hexagonal PQC nanoplates are then obtained by assuming that the layer interfaces are perfectly contacted. Numerical examples for six kinds of sandwich nanoplates made up of piezoelectric crystals (PE), quasicrystal (QC) and PQC are presented to illustrate the effect of the nonlocal parameter and stacking sequence of the nanoplates on the phonon, phason and electric fields, which play an important role in designing new composite structures in engineering.
This study presents a unique Mg-based alloy composition in the Mg–Zn–Yb system which exhibits bulk metallic glass, metastable icosahedral quasicrystals (iQCs), and crystalline approximant phases in ...the as-cast condition. Microscopy revealed a smooth gradual transition from glass to QC. We also report the complete melting of a metastable eutectic phase mixture (including a QC phase), generated via suppression of the metastable-to-stable phase transition at high heating rates using fast differential scanning calorimetry (FDSC). The melting temperature and enthalpy of fusion of this phase mixture could be measured directly, which unambiguously proves its metastability in any temperature range. The kinetic pathway from liquid state to stable solid state (an approximant phase) minimizes the free-energy barrier for nucleation through an intermediate state (metastable QC phase) because of its low solid–liquid interfacial energy. At high undercooling of the liquid, where diffusion is limited, another approximant phase with near-liquid composition forms just above the glass-transition temperature. These experimental results shed light on the competition between metastable and stable crystals, and on glass formation via system frustration associated with the presence of several free-energy minima.
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